Prove that cosecA+cotA=1/(cosecA-cotA) using the LHS of the identity?

provided that cosecA is not equal to cotA

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  • ted s
    Lv 7
    9 years ago
    Favorite Answer

    you have { LHS} 1 / sin A + cos A / sin A = [ 1+ cos A] / sin A =

    sin² A / { sin A [ 1 - cos A ] }= sin A / [ 1 - cos A ] = 1 / [ 1/sin A - cos A / sin A] =result

  • 9 years ago

    LHS: cosec A + cot A

    = ( 1 / sin A ) + ( cos A / sin A )

    = ( 1 + cos A ) / sin A

    .................................. multiply by [ ( 1 - cos A ) / sin A ] / [ ( 1 - cos A ) / sin A ]

    = [ ( 1 - cos ² A ) / sin ² A ] / [ ( 1 - cos A ) / sin A ]

    = ( sin ² A / sin ² A ) / [ ( 1 / sin A ) - ( cos A / sin A ) ]

    = 1 / ( cosec A - cot A ) ............ b i n g o ! ! !

  • 9 years ago

    cscA+cotA

    = cscA (1+cosA)

    = cscA(1-cos^2A)/(1-cosA)

    = cscA sin^2A/(1-cosA)

    = sinA/(1-cosA)

    = 1/(cscA - cotA)

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